Human learners, including infants, are highly sensitive to structure in their environment. Statistical learning refers to the process of extracting this structure. A major question in language acquisition in the past few decades has been the extent to which infants use statistical learning mechanisms to acquire their native language. There have been many demonstrations showing infants' ability to extract structures in linguistic input, such as the transitional probability between adjacent elements. This paper reviews current research on how statistical learning contributes to language acquisition. Current research is extending the initial findings of infants' sensitivity to basic statistical information in many different directions, including investigating how infants represent regularities, learn about different levels of language, and integrate information across situations. These current directions emphasize studying statistical language learning in context: within language, within the infant learner, and within the environment as a whole.